If your company has a no gun policy for employees that includes the property, then you can't have a gun on their property.
They can ask to search your vehicle, and you can refuse. But the most they can due is to fire you for violating company policy. Or fire you for not letting them search your vehicle.
Ohio is an "at will state". they don't need to find a gun in your car to fire you.
They can fire you for whatever reason they wish.
The posted no guns sign on the building applies to the general public, and would not include the parking lot....for the general public. And it is a civil manner. The property owner would have to take you to court, and prove damages for the ....general public.
But since you are an employee, you are bound by their rules.
Most people just keep their gun in the car, and your mouth shut. Don't tell your fellow workers.
If you contact HR, you may be opening a can of worms, since you asked, they will assume, and you could be under scrutiny.
You can ignore their policy, find a place to park off property, leave it at home, or take your chances leaving it in your car.